Trouble starting the engine?

Coolant temp sensor, fuel pressure, clean throttle body and idle control, check for vacuum leaks, scan for any unresolved fault codes, general tune, check all these first.

Check starter and battery connections.

If problem persists, remove starter and have it bench tested at most autoparts stores.

I have seen the Denso starter develop "dead spots" where it will do what you describe. Only fix is to replace it.